Question

Find six rational numbers between 5/6 and 3/4

Answer 1

Answer:

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Answer 2

Given:

Two rational numbers $\frac{5}{6}$ and $\frac{3}{4}$.

To Find:

Six rational numbers between $\frac{5}{6}$ and $\frac{3}{4}$.

Solution:

The denominators of the given rational numbers are 6 and 4. The LCM of 6 and 4 is 12.

Convert  $\frac{5}{6}$ and $\frac{3}{4}$ into like fractions.

$\frac{5\times 2} {6\times 2} =\frac{10}{12} \\\frac{3\times 3} {4\times 3} =\frac{9}{12}$

Since there is no rational number between $\frac{10}{12}$ and $\frac{9}{12}$ , multiply the numerator and denominator of both the rational numbers by 7. If any number less than 7 is taken then it will provide less than six rational numbers and if a number greater than 7 is taken, in that more than six rational numbers will be obtained.

$\frac{10\times 7} {12\times 7} =\frac{70}{84} \\\frac{9\times 7} {12\times 7} =\frac{63}{84}$

The six rational numbers between $\frac{63}{84}$ and $\frac{70}{84}$ are,

$\frac{64}{84}, \frac{65}{84}, \frac{66}{84}, \frac{67}{84}, \frac{68}{84}, \frac{69}{84}$

Thus, six rational numbers between  $\frac{5}{6}$ and $\frac{3}{4}$ are $\frac{64}{84}, \frac{65}{84}, \frac{66}{84}, \frac{67}{84}, \frac{68}{84}, \frac{69}{84}$.